A trade magazine routinely checks the drive-through service times of fast-food restaurants. Upper AA 9595% confidence interva
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Rewrite the second factor in the numerator as
Then in the entire integrand, set
, so that 
. The integral is then equivalent to
Note that by letting, we are enforcing an invertible substitution which would make it so that 
requires 
or 
. However, 
is positive over this first interval and negative over the second, so we can't ignore the absolute value.
So let's just assume the integral is being taken over a domain on which
so that 
. This allows us to write
We can show pretty easily that
which means the integral above becomes
Back-substituting to get this in terms of
is a bit of a nightmare, but you'll find that, since , we get
etc.
Then in the entire integrand, set
Note that by letting
So let's just assume the integral is being taken over a domain on which
We can show pretty easily that
which means the integral above becomes
Back-substituting to get this in terms of
etc.